Question

In a survey of 1118 U.S. adults conducted by the Financial Industry Regulatory Authority, 415 said they always pay their credit cards in full each month.

a) Construct a 95% interval for the population proportion of U.S. adults who pay their credit cards in full each month.

To show work, write out the following:
- The given numbers with their corresponding variables.

- The formula that's used to calculate the confidence interval. Also give a short explanation stating why you chose the formula that you did.

- The built in calculator program that you used to compute your answer.

b) Interpret you confidence interval from (a). Include the following:

- The confidence level.

- The population parameter of interest (in the context of the problem).

- The lower and upper bounds of the C.I., along with the units.

c) Based on your confidence interval from (a), is it true that a majority of U.S. adults always pay their credit cards in full each month? Explain why or why not using a complete sentence.

Answer 1

Given that in a survey of n = 1118 U.S. adults conducted by the Financial Industry Regulatory Authority, x = 415 said they always pay their credit cards in full each month.

a) 95% interval for the population proportion of U.S. adults who pay their credit cards in full each month is calculated as:

Where the sample proportion is calculated as:

Since the sample size is large enough that is greater than 30 hence we assume that the distribution is normal and the Z statistic is applicable for confidence interval calculation.

The Zc at 95% is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.975), thus the Zc at 95% is computed as 1.96.

Now the confidence interval is calculated as:

b) Interpretation:

With 95% confidence we can say that the true population proportion of U.S. adults who pay their credit cards in full each month lies between the calculated confidence interval.

The Population parameter of interest is the sample proportion that is:

Sample proportion = 0.371

The Lower Bound is 0.343 and the Upper bound is 0.400

c) To correct the statement that the majority of U.S. adults always pay their credit cards in full each month, we need to observe the calculated confidence interval that does it include the value greater than 0.50, because majority means the proportion greater than 0.50.

Now we observe that the Upper bound is 0.40 which is less than 0.50 hence it is not true to say that  a majority of U.S. adults always pay their credit cards in full each month.

Note: Feel free to ask if any query remains